derivative of (3+x-2x^2^{1/4})

Lösung

\frac{d}{d x} ((3 + x - 2 x^{2})^{\frac{1}{4}})

\frac{- 4 x + 1}{4 ( 3 + x - 2 x ^{2} ) ^{\frac{3}{4}}}

Schritte zur Lösung

\frac{d}{d x} ((3 + x - 2 x^{2})^{\frac{1}{4}})

Wende die Kettenregel an:

\frac{1}{4 ( 3 + x - 2 x ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (3 + x - 2 x^{2})

= \frac{1}{4 ( 3 + x - 2 x ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (3 + x - 2 x^{2})

\frac{d}{d x} (3 + x - 2 x^{2}) = - 4 x + 1

= \frac{1}{4 ( 3 + x - 2 x ^{2} ) ^{\frac{3}{4}}} (- 4 x + 1)

Vereinfache

\frac{1}{4 ( 3 + x - 2 x ^{2} ) ^{\frac{3}{4}}} (- 4 x + 1) : \frac{- 4 x + 1}{4 ( 3 + x - 2 x ^{2} ) ^{\frac{3}{4}}}

= \frac{- 4 x + 1}{4 ( 3 + x - 2 x ^{2} ) ^{\frac{3}{4}}}

im pl i c i t \frac{d y}{d x}, 4 x^{2} + 9 y^{2} = 36

y^{^{'}} + 2 x y = x e^{- x^{2}}

d er i v a t i v e 3 2690 - 10 x^{2}

\int 2 π x (x^{2} - 1)^{2} d x

\int_{4}^{9} \frac{4}{2 x} d x